Mathematics and Statistics Vol. 10(4), pp. 773 - 781
DOI: 10.13189/ms.2022.100408
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Double Duplication of Special Classes of Cycle Related Graphs

R.Kuppan , L.Shobana ^*
College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur-603 203, India

ABSTRACT

Let be a simple, finite, connected, plane graph with the vertex set , the edge set and the face set ). Martin Baca [1] defined, a connected plane graph with vertex set , edge set and face set to be face antimagic if there exists positive integers and and a bijection : such that the induced mapping : , where for a face , is the sum of all for all edges surrounding is also a bijection. This paper proves the existence of face antimagic labeling for the double duplication of all vertices by edges of gear graph for , grid graph for , where even, prism graph for and the double duplication of all vertices by edges of strong face of triangular snake graph for . The face antimagic labeling for double duplication of special graphs can be used to encrypt and decrypt the messages, which is used as a real time application. In [3], we used face antimagic labeling of strong face of duplication of all vertices by edges of a tree for to encrypt and decrypt thirteen secret numbers which can be extended to double duplication of graphs to encode and decode the numbers, which in turn can be used in military base, ATM and so on.

KEYWORDS
Double Duplication Graphs, Strong Face, Labeling, Face Anti-magic

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] R.Kuppan , L.Shobana , "Double Duplication of Special Classes of Cycle Related Graphs," Mathematics and Statistics, Vol. 10, No. 4, pp. 773 - 781, 2022. DOI: 10.13189/ms.2022.100408.

(b). APA Format:
R.Kuppan , L.Shobana (2022). Double Duplication of Special Classes of Cycle Related Graphs. Mathematics and Statistics, 10(4), 773 - 781. DOI: 10.13189/ms.2022.100408.